The Persian Calendar

The Persian calendar is a solar calendar with a starting point that matches that of the Islamic
calendar. Apart from that, the two calendars are not related. The origin of the Persian calendar can
be traced back to the 11th century when a group of astronomers (including the well-known poet Omar
Khayyam, pictured above) created what is known as the Jalaali calendar. However, a number of changes have been made
to the calendar since then.

The current calendar has been used in Iran since 1925 and in Afghanistan since 1957. However,
Afghanistan used the Islamic calendar in the years 1999-2002.

The Persian year starts at vernal equinox. If the astronomical vernal equinox falls before noon
(Tehran true time) on a particular day, then that day is the first day of the year. If the
astronomical vernal equinox falls after noon, the following day is the first day of the year.

Since the Persian year is defined by the astronomical vernal equinox, the answer is simply: Leap
years are years in which there are 366 days between two Persian new year’s days.

However, basing the Persian calendar purely on an astronomical observation of the vernal equinox
is rejected by many, and a few mathematical rules for determining the length of the year have been
suggested.

The most popular (and complex) of these is probably the following:

The calendar is divided into periods of 2820 years. These periods are
then divided into 88 cycles whose lengths follow this pattern:

29, 33, 33, 33, 29, 33, 33, 33, 29, 33, 33, 33, ...

This gives 2816 years. The total of 2820 years is achieved by extending the last cycle by 4 years
(for a total of 37 years).

If you number the years within each cycle starting with 0, then leap years are the years that are
divisible by 4, except that the year 0 is not a leap year.

So within, say, a 29 year cycle, this is the leap year pattern:

Year

Type

Year

Type

Year

Type

Year

Type

0

Ordinary

8

Leap

16

Leap

24

Leap

1

Ordinary

9

Ordinary

17

Ordinary

25

Ordinary

2

Ordinary

10

Ordinary

18

Ordinary

26

Ordinary

3

Ordinary

11

Ordinary

19

Ordinary

27

Ordinary

4

Leap

12

Leap

20

Leap

28

Leap

5

Ordinary

13

Ordinary

21

Ordinary

6

Ordinary

14

Ordinary

22

Ordinary

7

Ordinary

15

Ordinary

23

Ordinary

This gives a total of 683 leap years every 2820 years, which corresponds to an average year
length of 365 683/2820 = 365.24220 days. This is a better approximation to the
tropical year than the 365.2425 days of the Gregorian calendar.

The current 2820 year period started in the year AP 475 (AD 1096).

This “mathematical” calendar currently coincides closely with the purely astronomical
calendar. In the years between AP 1244 and 1531 (AD 1865 and 2152) a discrepancy of one
day is seen twice, namely in AP 1404 and 1437 (starting at vernal equinox of AD 2025 and
2058). However, outside this period, discrepancies are more frequent.